Fast digital/analog converters are required in modern communication systems for a large number of applications. In a conventional approach, the digital word having a length of N bits is converted into an analog signal. This is done by providing a digital/analog converter which comprises 2N different signal levels as comparison and threshold values. Depending on the comparison, a corresponding analog output signal is then produced. However, this approach results in significant power consumption and a very large amount of space being taken up, since for each additional bit of resolution the number of threshold levels needs to be doubled. By way of example, a digital word having a length of 8 bits (N=8) can take up a total of 255 different analog signal levels. A digital word having a bit length of 9 bits (N=9) can be used to represent 512 analog values.
For this reason, modern converters very frequently sample the digital word using a very high clock signal and process the resultant signal further using a noise shaping method. This process is known generally as “noise shaping”.
FIG. 5 shows a digital/analog converter operating on the basis of the known principle. In this case, the digital word or the digital signal D having a bit length N is supplied to a noise shaper. The noise shaper samples the digital word D at a much higher frequency Fs than that of the digital data and produces a second digital word having the bit length M therefrom. The second digital word having the bit length M<N is supplied to the actual digital/analog converter DAC and is converted into an analog signal.
On account of the noise shaping, the conversion of the digital word D having the bit length N which is applied to the input into the digital word having the bit length M results in an improvement in the signal-to-noise ratio within a certain useful bandwidth relative to the bit length M. The useful bandwidth corresponds to the bit length N of the first digital data word D. The oversampling within the noise shaper moves a noise component of the digital data word applied to the input into higher frequency ranges and hence outside of the useful band spectrum.
This process is illustrated by the diagrams shown in FIG. 5. The data word D applied to the input contains the signal component and also a noise component (not shown here) which, in the present case, is white noise having a constant component. At the integer multiple sampling frequencies Fs of the noise shaper, repetition spectra for the data words applied to the input are produced. At the output, the data word with the bit length M which is output accordingly has “repetition spectra” for the digital word D at the frequencies Fs, 2Fs, etc. In addition, the noise shaping at half the sampling frequency Fs/2 produces a noise component which is moved into the higher frequency ranges by the noise shaper.
The data word converted in the noise shaper is now supplied to the actual digital/analog converter, which produces an analog signal therefrom. On account of the response sin (x)/x of the hold element, the conversion results simultaneously in additional attenuation for higher spectral components at the sampling frequency Fs and also the associated harmonic frequencies. These higher components are then rejected in a low-pass filter, and the output produces the converted analog signal with a relatively small noise component.
The noise components which the noise shaper moves into higher frequency ranges are then rejected by the low-pass filter. The resolution of the noise shaper and also of the digital/analog converter is better the higher the bit length M of the second data word. Equally, the order of the noise shaper and the oversampling rate need to be taken into account.
In this context, however, the linear response-of the digital/analog converter DAC needs to be taken into account. Nonlinear components in the response produce additional intermodulation products. These can result in the noise component which the noise shaper moves into higher frequency ranges being convoluted back into the required frequency band. This impairs the signal-to-noise ratio in the useful band.
Particularly in the case of digital/analog converters for audio applications, these intermodulation products can be adopted in the output signal as interfering noise. Implementing a very linear digital/analog converter is very complex, however, and results in additional costs.